TSTP Solution File: MGT026-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : MGT026-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 13:54:09 EDT 2024

% Result   : Unsatisfiable 0.15s 0.39s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   60 (  16 unt;   0 def)
%            Number of atoms       :  158 (  41 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  169 (  71   ~;  98   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-4 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   34 (  34   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f114,plain,
    $false,
    inference(subsumption_resolution,[],[f113,f17]) ).

fof(f17,axiom,
    greater(sk2,critical_point(sk1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8_44) ).

fof(f113,plain,
    ~ greater(sk2,critical_point(sk1)),
    inference(forward_demodulation,[],[f110,f104]) ).

fof(f104,plain,
    critical_point(sk1) = appear(efficient_producers,sk1),
    inference(unit_resulting_resolution,[],[f98,f51]) ).

fof(f51,plain,
    ( greater(cardinality_at_time(efficient_producers,sk2),zero)
    | critical_point(sk1) = appear(efficient_producers,sk1) ),
    inference(subsumption_resolution,[],[f50,f15]) ).

fof(f15,axiom,
    environment(sk1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8_42) ).

fof(f50,plain,
    ( ~ environment(sk1)
    | greater(cardinality_at_time(efficient_producers,sk2),zero)
    | critical_point(sk1) = appear(efficient_producers,sk1) ),
    inference(subsumption_resolution,[],[f48,f16]) ).

fof(f16,axiom,
    in_environment(sk1,sk2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8_43) ).

fof(f48,plain,
    ( ~ in_environment(sk1,sk2)
    | ~ environment(sk1)
    | greater(cardinality_at_time(efficient_producers,sk2),zero)
    | critical_point(sk1) = appear(efficient_producers,sk1) ),
    inference(resolution,[],[f14,f43]) ).

fof(f43,plain,
    ( greater_or_equal(sk2,appear(efficient_producers,sk1))
    | critical_point(sk1) = appear(efficient_producers,sk1) ),
    inference(resolution,[],[f39,f10]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ~ greater(X0,X1)
      | greater_or_equal(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_37) ).

fof(f39,plain,
    ( greater(sk2,appear(efficient_producers,sk1))
    | critical_point(sk1) = appear(efficient_producers,sk1) ),
    inference(resolution,[],[f33,f30]) ).

fof(f30,plain,
    ! [X0] :
      ( ~ greater(critical_point(sk1),X0)
      | greater(sk2,X0) ),
    inference(resolution,[],[f8,f17]) ).

fof(f8,axiom,
    ! [X2,X0,X1] :
      ( ~ greater(X0,X1)
      | ~ greater(X1,X2)
      | greater(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity_35) ).

fof(f33,plain,
    ( greater(critical_point(sk1),appear(efficient_producers,sk1))
    | critical_point(sk1) = appear(efficient_producers,sk1) ),
    inference(resolution,[],[f9,f24]) ).

fof(f24,plain,
    greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1)),
    inference(unit_resulting_resolution,[],[f15,f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( ~ environment(X0)
      | greater_or_equal(critical_point(X0),appear(efficient_producers,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_critical_point_after_EP_34) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ~ greater_or_equal(X0,X1)
      | X0 = X1
      | greater(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_36) ).

fof(f14,axiom,
    ! [X0,X1] :
      ( ~ greater_or_equal(X1,appear(efficient_producers,X0))
      | ~ in_environment(X0,X1)
      | ~ environment(X0)
      | greater(cardinality_at_time(efficient_producers,X1),zero) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_41) ).

fof(f98,plain,
    ~ greater(cardinality_at_time(efficient_producers,sk2),zero),
    inference(unit_resulting_resolution,[],[f15,f28,f18,f26,f90,f2]) ).

fof(f2,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ subpopulation(X1,X0,X2)
      | ~ environment(X0)
      | ~ subpopulation(X3,X0,X2)
      | selection_favors(X1,X3,X2)
      | zero != cardinality_at_time(X3,X2)
      | ~ greater(cardinality_at_time(X1,X2),zero) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp2_favour_members_29) ).

fof(f90,plain,
    zero = cardinality_at_time(first_movers,sk2),
    inference(subsumption_resolution,[],[f89,f87]) ).

fof(f87,plain,
    ( greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2))
    | zero = cardinality_at_time(first_movers,sk2) ),
    inference(subsumption_resolution,[],[f86,f15]) ).

fof(f86,plain,
    ( zero = cardinality_at_time(first_movers,sk2)
    | ~ environment(sk1)
    | greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) ),
    inference(subsumption_resolution,[],[f84,f17]) ).

fof(f84,plain,
    ( zero = cardinality_at_time(first_movers,sk2)
    | ~ greater(sk2,critical_point(sk1))
    | ~ environment(sk1)
    | greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) ),
    inference(resolution,[],[f82,f20]) ).

fof(f20,plain,
    ! [X2,X0] :
      ( ~ subpopulations(first_movers,efficient_producers,X0,X2)
      | ~ greater(X2,critical_point(X0))
      | ~ environment(X0)
      | greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
    inference(equality_resolution,[],[f13]) ).

fof(f13,axiom,
    ! [X2,X0,X1] :
      ( ~ environment(X0)
      | ~ greater(X2,X1)
      | critical_point(X0) != X1
      | ~ subpopulations(first_movers,efficient_producers,X0,X2)
      | greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_40) ).

fof(f82,plain,
    ( subpopulations(first_movers,efficient_producers,sk1,sk2)
    | zero = cardinality_at_time(first_movers,sk2) ),
    inference(subsumption_resolution,[],[f79,f36]) ).

fof(f36,plain,
    ( greater(cardinality_at_time(first_movers,sk2),zero)
    | zero = cardinality_at_time(first_movers,sk2) ),
    inference(resolution,[],[f34,f9]) ).

fof(f34,plain,
    greater_or_equal(cardinality_at_time(first_movers,sk2),zero),
    inference(unit_resulting_resolution,[],[f16,f15,f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( ~ in_environment(X0,X1)
      | ~ environment(X0)
      | greater_or_equal(cardinality_at_time(first_movers,X1),zero) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_first_movers_exist_31) ).

fof(f79,plain,
    ( zero = cardinality_at_time(first_movers,sk2)
    | ~ greater(cardinality_at_time(first_movers,sk2),zero)
    | subpopulations(first_movers,efficient_producers,sk1,sk2) ),
    inference(resolution,[],[f78,f56]) ).

fof(f56,plain,
    ( ~ greater(cardinality_at_time(efficient_producers,sk2),zero)
    | ~ greater(cardinality_at_time(first_movers,sk2),zero)
    | subpopulations(first_movers,efficient_producers,sk1,sk2) ),
    inference(subsumption_resolution,[],[f55,f15]) ).

fof(f55,plain,
    ( ~ environment(sk1)
    | ~ greater(cardinality_at_time(first_movers,sk2),zero)
    | ~ greater(cardinality_at_time(efficient_producers,sk2),zero)
    | subpopulations(first_movers,efficient_producers,sk1,sk2) ),
    inference(resolution,[],[f3,f16]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( ~ in_environment(X0,X1)
      | ~ environment(X0)
      | ~ greater(cardinality_at_time(first_movers,X1),zero)
      | ~ greater(cardinality_at_time(efficient_producers,X1),zero)
      | subpopulations(first_movers,efficient_producers,X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep_30) ).

fof(f78,plain,
    ( greater(cardinality_at_time(efficient_producers,sk2),zero)
    | zero = cardinality_at_time(first_movers,sk2) ),
    inference(subsumption_resolution,[],[f77,f16]) ).

fof(f77,plain,
    ( ~ in_environment(sk1,sk2)
    | greater(cardinality_at_time(efficient_producers,sk2),zero)
    | zero = cardinality_at_time(first_movers,sk2) ),
    inference(resolution,[],[f75,f22]) ).

fof(f22,plain,
    greater_or_equal(sk2,critical_point(sk1)),
    inference(unit_resulting_resolution,[],[f17,f10]) ).

fof(f75,plain,
    ! [X0] :
      ( ~ greater_or_equal(X0,critical_point(sk1))
      | ~ in_environment(sk1,X0)
      | greater(cardinality_at_time(efficient_producers,X0),zero)
      | zero = cardinality_at_time(first_movers,sk2) ),
    inference(subsumption_resolution,[],[f73,f15]) ).

fof(f73,plain,
    ! [X0] :
      ( ~ greater_or_equal(X0,critical_point(sk1))
      | ~ in_environment(sk1,X0)
      | ~ environment(sk1)
      | greater(cardinality_at_time(efficient_producers,X0),zero)
      | zero = cardinality_at_time(first_movers,sk2) ),
    inference(superposition,[],[f14,f65]) ).

fof(f65,plain,
    ( critical_point(sk1) = appear(efficient_producers,sk1)
    | zero = cardinality_at_time(first_movers,sk2) ),
    inference(subsumption_resolution,[],[f64,f62]) ).

fof(f62,plain,
    ( greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2))
    | zero = cardinality_at_time(first_movers,sk2)
    | critical_point(sk1) = appear(efficient_producers,sk1) ),
    inference(subsumption_resolution,[],[f61,f15]) ).

fof(f61,plain,
    ( critical_point(sk1) = appear(efficient_producers,sk1)
    | zero = cardinality_at_time(first_movers,sk2)
    | ~ environment(sk1)
    | greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) ),
    inference(subsumption_resolution,[],[f59,f17]) ).

fof(f59,plain,
    ( critical_point(sk1) = appear(efficient_producers,sk1)
    | zero = cardinality_at_time(first_movers,sk2)
    | ~ greater(sk2,critical_point(sk1))
    | ~ environment(sk1)
    | greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) ),
    inference(resolution,[],[f58,f20]) ).

fof(f58,plain,
    ( subpopulations(first_movers,efficient_producers,sk1,sk2)
    | critical_point(sk1) = appear(efficient_producers,sk1)
    | zero = cardinality_at_time(first_movers,sk2) ),
    inference(resolution,[],[f57,f36]) ).

fof(f57,plain,
    ( ~ greater(cardinality_at_time(first_movers,sk2),zero)
    | subpopulations(first_movers,efficient_producers,sk1,sk2)
    | critical_point(sk1) = appear(efficient_producers,sk1) ),
    inference(resolution,[],[f56,f51]) ).

fof(f64,plain,
    ( critical_point(sk1) = appear(efficient_producers,sk1)
    | zero = cardinality_at_time(first_movers,sk2)
    | ~ greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) ),
    inference(subsumption_resolution,[],[f63,f15]) ).

fof(f63,plain,
    ( critical_point(sk1) = appear(efficient_producers,sk1)
    | zero = cardinality_at_time(first_movers,sk2)
    | ~ environment(sk1)
    | ~ greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) ),
    inference(subsumption_resolution,[],[f60,f18]) ).

fof(f60,plain,
    ( critical_point(sk1) = appear(efficient_producers,sk1)
    | zero = cardinality_at_time(first_movers,sk2)
    | selection_favors(efficient_producers,first_movers,sk2)
    | ~ environment(sk1)
    | ~ greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) ),
    inference(resolution,[],[f58,f1]) ).

fof(f1,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ subpopulations(X1,X2,X0,X3)
      | selection_favors(X2,X1,X3)
      | ~ environment(X0)
      | ~ greater(growth_rate(X2,X3),growth_rate(X1,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates_28) ).

fof(f89,plain,
    ( zero = cardinality_at_time(first_movers,sk2)
    | ~ greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) ),
    inference(subsumption_resolution,[],[f88,f15]) ).

fof(f88,plain,
    ( zero = cardinality_at_time(first_movers,sk2)
    | ~ environment(sk1)
    | ~ greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) ),
    inference(subsumption_resolution,[],[f85,f18]) ).

fof(f85,plain,
    ( zero = cardinality_at_time(first_movers,sk2)
    | selection_favors(efficient_producers,first_movers,sk2)
    | ~ environment(sk1)
    | ~ greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)) ),
    inference(resolution,[],[f82,f1]) ).

fof(f26,plain,
    subpopulation(first_movers,sk1,sk2),
    inference(unit_resulting_resolution,[],[f16,f15,f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( ~ in_environment(X0,X1)
      | ~ environment(X0)
      | subpopulation(first_movers,X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_32) ).

fof(f18,axiom,
    ~ selection_favors(efficient_producers,first_movers,sk2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l8_45) ).

fof(f28,plain,
    subpopulation(efficient_producers,sk1,sk2),
    inference(unit_resulting_resolution,[],[f16,f15,f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ~ in_environment(X0,X1)
      | ~ environment(X0)
      | subpopulation(efficient_producers,X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_33) ).

fof(f110,plain,
    ~ greater(sk2,appear(efficient_producers,sk1)),
    inference(unit_resulting_resolution,[],[f106,f10]) ).

fof(f106,plain,
    ~ greater_or_equal(sk2,appear(efficient_producers,sk1)),
    inference(unit_resulting_resolution,[],[f15,f16,f98,f14]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : MGT026-1 : TPTP v8.1.2. Released v2.4.0.
% 0.14/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n021.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Apr 30 03:42:10 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.37  % (4612)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (4615)WARNING: value z3 for option sas not known
% 0.15/0.38  % (4613)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (4614)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (4616)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (4615)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38  % (4619)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38  % (4617)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38  % (4618)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.39  TRYING [1]
% 0.15/0.39  TRYING [2]
% 0.15/0.39  % (4619)First to succeed.
% 0.15/0.39  TRYING [3]
% 0.15/0.39  TRYING [1]
% 0.15/0.39  % (4619)Refutation found. Thanks to Tanya!
% 0.15/0.39  % SZS status Unsatisfiable for theBenchmark
% 0.15/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39  % (4619)------------------------------
% 0.15/0.39  % (4619)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.39  % (4619)Termination reason: Refutation
% 0.15/0.39  
% 0.15/0.39  % (4619)Memory used [KB]: 839
% 0.15/0.39  % (4619)Time elapsed: 0.007 s
% 0.15/0.39  % (4619)Instructions burned: 8 (million)
% 0.15/0.39  % (4619)------------------------------
% 0.15/0.39  % (4619)------------------------------
% 0.15/0.39  % (4612)Success in time 0.023 s
%------------------------------------------------------------------------------